Equations : Fractions

Question

Equation : 

6x-2   5x+9 =

____+ _____     -5

  5         6

 

or if it makes it easier: ((6x-2) / 5) + ((5x+9)/6) = -5

 

I need to know how to work it out, why and what the answer is. Please reply quick :)

Answer 1

Since we have an equation, we want to solve for the variable x.  This equation has fractional terms, so we want to use the LCD.  The LCD  of the equation is 30.

 

 

[6(6x - 2) + 5(5x + 9)] / 30 = -150 / 30

 

 

Since the denominators are now equal, we only need to equate the numerators.  This makes the equation easier to solve.

 

6(6x - 2) + 5(5x + 9) = -150

 

 

Distribute terms to get rid of parentheses.

 

36x - 12 + 25x + 45 = -150

 

 

Combine like terms.

 

61x + 33 = -150

 

 

Subtract 33 on both sides of equation.

 

61x = -183

 

   x = -3

 

 

To check, we plug in this value of x into the equation.  If the left side equals the right side, then the solution is correct.

 

((-18 - 2) / 5) + ((-15 + 9) / 6) = -5

 

(-20 / 5) + (-6 / 6) = -5

 

-4 + (-1) = -5

 

-4 - 1 = -5

 

  -5 = -5

 

 

It checks!  :)